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07 mid sol

# 07 mid sol - Economics 109 Midterm Examination I Answer...

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Unformatted text preview: Economics 109 Midterm Examination I Answer Sheet, Fall 2007, Prof. Watson Your student ID: Version: 2. Number of strategies that player 1 has (circle one): 1 2 3 4 5 @ 7 8 10 16 64 256 t 4,5 2,2 5,2 “3” m 1,3 8,5 1,2 €~ b 2,1 3,2 5,2 '3“ ~ Player 1's best response: ‘1': 4. l 2 X Y “we 3f+304>>>4r (p) K 8,2 0’0 My of+§0~p>>3 Cir?) L 3,0 5,1 (F) 5‘? >44 §f<2 M 4,2 3,2 L ,L wrgm Feta?) Istominated? Circle one: @ NO If so, name a strategy that dominates it: /@ﬂ ( P , I ' f , o > “FEW W7 3) 6 (EL 1 3;) 1 If not, name a belief to which M is a best response: 2 \ 1 a b c E w 8,2 24 8 x 62 4,3 4,4 y 11 3,3 9,2 (a) The efﬁcient strategy proﬁles are: ( w l C) M ( 7/ C) (b) The rationalizable set is: R = { x, x { b , a} (a) Best-response functions 9% - ‘5”; 5'" ‘Zx = (=3 x : ’37 X: 612(3)“? 221-: 10+ 76—2750 (b) Rationalizable set: Br es is: (X,?<,><,></ , b One of the rational'zable st ate roﬁl ( ) 1 r jy p ,__> ﬁll/tam X/X/ X/X/ (c) Values of m that can arise in a rationalizable outéome: u Economics 109 Midterm Examination 11 Answer Sheet, Fall 2007, Prof. Watson Version: 2. Circle the cells that are pure-strategy Nash equilibria and put an asterisk (*) in the cell of each efﬁcient Nash equilibrium. P X 8,2 () lg?=§} qr=g_ (PP) y 0,3 ZP+3-?F=5p+l*f 2.. wimfwugy Z :5? ’ P5? ~24 ﬂ ' iv.vz+><Yz-Y.z ) 4YL-4K‘lr 2w: ~73 O . l_______i P Wop/\culaams '0 NM «1. \$5231“; : 212-27, so => 3 Y.= 6%» Y; :::= + +X"Z_Y-‘Zyz 5 => 72: gzz(\l‘): Z’ZX’Y' 9/0170! is, 573.. Par-Hf in Wng 54’! W 7c an: I‘s 2(I—x)z+ x04xl- (bx); : G—x3L-r x(l—x)= (I-x)(u—x«~x)= l~x A"’ H“- lMHJ M; VIM)“ L elm"? Equilibrium strategy proﬁle: mh +1> 14* IMS'I’ ’30:th x, WA |S‘ 0. 5. go“ : 2+2132’ ZS, 5:0 =7 S’=8Rl(SL)= Has; 2 S, awe = 2+ZASI-ZSL=O '? SL=E£L(S|)='+aSI 33; SL L S 8% 5 8‘1‘ ‘ sit. Bk ‘ 32. I I 6R1, S. 9’ S: l a Re (0") a>l a = o (a) Is there an a such that the game has no Nash equilibrium? Circle one: Ifyes, a; I (b) Is there an a such that the game has an efﬁcient Nash equilibrium? Circle one: @ NO Ifyes, a = C Your comments on the course so far: ...
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07 mid sol - Economics 109 Midterm Examination I Answer...

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